The electrical power steering system of this type is disclosed in, for example, Patent Literature 1. In the electrical power steering system disclosed in Patent Literature 1, a casing of the electrical motor (motor housing) is rotatably assembled onto a housing of the steering apparatus (gear housing), and a rotational center of the casing (motor housing) is separated from a rotational center of the driving pulley by a predetermined amount. Therefore, through rotation of the casing (motor housing) relative to the housing (gear housing), a separation distance between the driving pulley and the driven pulley can be adjusted, and thus a tension of the belt can be adjusted.